Automated Market Making and Loss-Versus-Rebalancing

Abstract:
We consider the market microstructure of constant function market makers (CFMMs) from the perspective of passive liquidity providers (LPs). In a Black-Scholes setting, we compare the CFMM’s performance to that of a rebalancing strategy, which replicates the CFMM’s trades at market prices. The CFMM systematically underperforms the rebalancing strategy, because it executes all trades at worse-than-market prices. The performance gap between the two strategies, “loss-versus-rebalancing” (LVR, pronounced “lever”), depends on the volatility of the underlying asset and the marginal liquidity of the CFMM bonding function. Our model’s expressions for CFMM losses match actual losses from the Uniswap v2 WETH-USDC pair. LVR provides tradeable insight in both the ex ante and ex post assessment of CFMM LP investment decisions, and can also inform the design of CFMM protocols.